 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...right angles. Use the diagram of (209), and complete the demonstration by (45). PROPOSITION XXXIV. 211. THEOREM. The sum of the angles of a spherical triangle is greater than 180° and less than 5J THE ELEMENTS OF SOLID GEOMETRY. Now, A = 180° - B'C' . . . (205) and B = 180°... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...sides of a convex spherical polygon is less than 360°, or four right angles. PROPOSITION XXVII. 688. Theorem. The sum of the angles of a spherical triangle...greater than two and less than six right angles. Let ABC represent a spherical triangle. To prove that the sum 0} the angles А, В and С is greater than... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...sides of a convex spherical polygon is less than the circumference of a great circle. PROPOSITION XXVI. The sum of the angles of a spherical triangle is greater than two and less than six right angles. PROPOSITION XXVII. Two symmetrical spherical triangles are equal in area. PROPOSITION XXVIII. PROPOSITION... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...AC > BC. In like manner, we may prove AB + BC > AC, and AC + BC > AB. PROPOSITION XV. THEOREM. 621. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. To prove A + B + C > 180°, and < 540'°. Let A'B'C' be the polar triangle of ABC, and denote its sides... | |
 | American Mathematical Society - Mathematics - 1905 - 1032 pages
...the triangle can be read off as L. e., p. 595. pure spherics. The proof of the theorem (§ 567) — the sum of the angles of a spherical triangle is greater than two and less than six right angles — assumes that a spherical triangle is always positive. The theorem can be proved in the usual way... | |
 | Ephraim Miller - Plane trigonometry - 1894 - 222 pages
...90°. REMARK II. The functions of £a, $b, and $c, in [57] and [59], are real quantities. For since the sum of the angles of a spherical triangle is greater than 180°, and less than six right angles, then S, or $(A + В + C)- in [57] and [59], is greater than... | |
 | John Macnie - Geometry - 1895 - 386 pages
...the side of A'B'C' that is opposite ZA, etc., we have the relations : PROPOSITION XV. THEOREM. 633. The sum, of the angles of a spherical triangle* is...greater than two, and less than six, right angles. Given: A, B, C, the angles of a spherical triangle ABC; To Prove : Z A+^ B+Z C> 180° and < 540°.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that the sum of the angles of a spherical triangle is greater than a straight angle*. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that the sum of the angles of a spherical triangle is greater than a straight angle. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...the area of any spherical polygon, the angles of which are given. NOTE. — It has been shown that the sum of the angles of a spherical triangle is greater than 180°: The amount, in degrees, by which the sum of the angles exceeds 180°, is called the spherical... | |
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The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... 
